Coefficient and Fekete-Szegö problem estimates for certain subclass of analytic and bi-univalent functions

Abstract

In this paper, we obtain the Fekete-Szeg? problem for the k-th (k ? 1) root transform of the analytic and normalized functions f satisfying the condition 1+ ? ??/2sin? < Re{z f'(z)/f(z)) < 1+ ?/2sin? (|z| < 1), where ? ? [?/2,?). Afterwards, by the above two-sided inequality we introduce a certain subclass of analytic and bi-univalent functions in the disk |z| < 1 and obtain upper bounds for the first few coefficients and Fekete-Szeg? problem for functions f belonging to this class.